rsarashi wrote:Of the 300 subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects, how many of the subjects experienced only one of these effects?

A. 105
B. 125
C. 130
D. 180
E. 195

OAD

Hi rsarashi,

This is a typical question based on the application of Venn diagram.

Pl. find the formula for overlapping sets.

S or V or Z = S + V + Z - [(S and V) + (S and Z) +(V and Z)] - 2*(S and V and Z);

Total number of participants = S + V + Z - Participants who experienced only two effects - 2*Participants who experienced all the three effects

Where,

S or V or Z = The total number of participated = 300; since it is given that AT LEAST one participants experienced one of the three effects, S or V or Z = 300. Otherwise, we would have to deduct the number of those who did not experience any of the three effects.

S = Number of participants who experienced sweaty palms;

V = Number of participants who experienced vomiting;

Z = Number of participants who experienced dizziness

Since the data are in percents, we would deal with percent figure and then would take into account the actual number of participants = 300

We have,

Total number of participants = S + V + Z - Participants who experienced only two effects - 2*Participants who experienced all the three effects

=> 100 = 40 + 30 + 75 - 35 - 2*Participants who experienced all the three effects

=> Participants who experienced all the three effects = 5%

Thus, we have,

Participants who experienced only two effects = 35%

Participants who experienced all the three effects = 5%

Thus, Participants who experienced only one of the three effects = 100% - 35% - 5% = 60%

Or, Participants who experienced only one of the three effects = 300*(60/100) = 180.

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

-Jay
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